Question

as part of an exercise regimen you walk 9 miles on an indoor track. then you jog at three times your walking speed for another 9 miles. if the total time spent walking and jogging is 4 hours, find the walking and jogging rates

Answer 1

Rate of walking is
`3 \ mi/hr` and Rate of Jogging is
`9\ mi/hr`.

Explanation:

Given:

Total time = 4 hours

Jogging distance = 9 miles

walking distance = 9 miles

We need to find the walking and jogging rates.

Solution:

Let the walking rate be 'x'.

Now given that;

Jogging rate is 3 times faster than walking rate.

Jogging rate =
`3x`

Now we know that;

Time is equal to distance divided by speed.

Time for walking =
`(9)/(x)`

Time for Jogging =
`(9)/(3x) = (3)/(x)`

Now we know that:

Total time is equal to sum of Time for walking and Time for Jogging.

framing in equation form we get;

`(9)/(x)+(3)/(x)=4\\\\(9+3)/(x)=4\\\\(12)/(x)=4\\\\(12)/(4)=x\\\\x =3\ mi/hr`

Rate of walking =
`3 \ mi/hr`

Rate of Jogging =
`3x=3*3 = 9 \ mi/hr`

Hence Rate of walking is
`3 \ mi/hr` and Rate of Jogging is
`9\ mi/hr`.